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1. Given-data probabilistic fatigue assessment for offshore wind turbines using Bayesian quadrature

Author

Elias Fekhari, Vincent Chabridon, Joseph Muré, and Bertrand Iooss

Subjects
design of experiments, fatigue loads, kernel herding, uncertainty propagation, wind turbine, Engineering (General). Civil engineering (General), TA1-2040
Abstract

Offshore wind turbines intend to take a rapidly growing share in the electric mix. The design, installation, and exploitation of these industrial assets are regulated by international standards, providing generic guidelines. Constantly, new projects reach unexploited wind resources, pushing back installation limits. Therefore, turbines are increasingly subject to uncertain environmental conditions, making long-term investment decisions riskier (at the design or end-of-life stage). Fortunately, numerical models of wind turbines enable to perform accurate multi-physics simulations of such systems when interacting with their environment. The challenge is then to propagate the input environmental uncertainties through these models and to analyze the distribution of output variables of interest. Since each call of such a numerical model can be costly, the estimation of statistical output quantities of interest (e.g., the mean value, the variance) has to be done with a restricted number of simulations. To do so, the present paper uses the kernel herding method as a sampling technique to perform Bayesian quadrature and estimate the fatigue damage. It is known from the literature that this method guarantees fast and accurate convergence together with providing relevant properties regarding subsampling and parallelization. Here, one numerically strengthens this fact by applying it to a real use case of an offshore wind turbine operating in Teesside, UK. Numerical comparison with crude and quasi-Monte Carlo sampling demonstrates the benefits one can expect from such a method. Finally, a new Python package has been developed and documented to provide quick open access to this uncertainty propagation method.

Published
2024
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2. Functional Outlier Detection by Means of h-Mode Depth and Dynamic Time Warping

Author

Álvaro Rollón de Pinedo, Mathieu Couplet, Bertrand Iooss, Nathalie Marie, Amandine Marrel, Elsa Merle, and Roman Sueur

Subjects
functional data analysis, functional outlier detection, probabilistic modeling, computer experiments, sensitivity analysis, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999
Abstract

Finding outliers in functional infinite-dimensional vector spaces is widely present in the industry for data that may originate from physical measurements or numerical simulations. An automatic and unsupervised process of outlier identification can help ensure the quality of a dataset (trimming), validate the results of industrial simulation codes, or detect specific phenomena or anomalies. This paper focuses on data originating from expensive simulation codes to take into account the realistic case where only a limited quantity of information about the studied process is available. A detection methodology based on different features, such as h-mode depth or the dynamic time warping, is proposed to evaluate the outlyingness both in the magnitude and shape senses. Theoretical examples are used to identify pertinent feature combinations and showcase the quality of the detection method with respect to state-of-the-art methodologies of detection. Finally, we show the practical interest of the method in an industrial context thanks to a nuclear thermal-hydraulic use case and how it can serve as a tool to perform sensitivity analysis on functional data.

Published
2021
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4. Atmospheric Transport Modeling with 3D Lagrangian Dispersion Codes Compared with SF6 Tracer Experiments at Regional Scale

Author

François Van Dorpe, Bertrand Iooss, Vladimir Semenov, Olga Sorokovikova, Alexey Fokin, and Yves Margerit

Subjects
Electrical engineering. Electronics. Nuclear engineering, TK1-9971
Abstract

The results of four gas tracer experiments of atmospheric dispersion on a regional scale are used for the benchmarking of two atmospheric dispersion modeling codes, MINERVE-SPRAY (CEA), and NOSTRADAMUS (IBRAE). The main topic of this comparison is to estimate the Lagrangian code capability to predict the radionuclide atmospheric transfer on a large field, in the case of risk assessment of nuclear power plant for example. For the four experiments, the results of calculations show a rather good agreement between the two codes, and the order of magnitude of the concentrations measured on the soil is predicted. Simulation is best for sampling points located ten kilometers from the source, while we note a divergence for more distant points results (difference in concentrations by a factor 2 to 5). This divergence may be explained by the fact that, for these four experiments, only one weather station (near the point source) was used on a field of 10 000 km2, generating the simulation of a uniform wind field throughout the calculation domain.

Published
2007
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24. Variance-based importance measures for machine learning model interpretability

Author

Bertrand, Iooss, Chabridon, Vincent, Vincent, Thouvenot, Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Saclay Industrial Lab for Artificial Intelligence Research (SINCLAIR AI Lab), THALES [France]-TOTAL FINA ELF-EDF (EDF), and Thales SIX GTS France

Subjects
statistical learning, [SPI]Engineering Sciences [physics], sensitivity analysis, Shapley effects, interpretability, Sobol' indices
Abstract

International audience; Machine learning algorithms benefit from an unprecedented boost in the industrial world, in particular in support of decision-making for critical systems. However, their lack of "interpretability" remains a challenge to leverage in order to make these tools fully intelligible and auditable. This paper aims to track and synthesize of a panel of interpretability metrics (called "importance measures") whose aim is to quantify the impact of each predictor on the statistical model's output variance. It is shown that the choice of a relevant metric has to be guided by proper constraints imposed by the data and the considered model (linear vs. nonlinear phenomenon of interest, input dimension, input dependency) together with taking the type of study the user wants to perform into consideration (detect influential variables, rank them, etc.). Finally, these metrics are estimated and analyzed on a public dataset so as to illustrate some of their theoretical and empirical properties.

Published
2022

29. Unlocking Large Scale Uncertainty Quantification with In Transit Iterative Statistics

Author

Alejandro Ribés, Théophile Terraz, Yvan Fournier, Bertrand Iooss, Bruno Raffin, EDF R&D (EDF R&D), EDF (EDF), Data Aware Large Scale Computing (DATAMOVE ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Informatique de Grenoble (LIG), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)

Subjects
[INFO]Computer Science [cs]
Abstract

International audience; Multi-run numerical simulations using supercomputers are increasingly used by physicists and engineers for dealing with input data and model uncertainties. Most of the time, the input parameters of a simulation are modeled as random variables, then simulations are run a (possibly large) number of times with input parameters varied according to a specific design of experiments. Uncertainty quantification for numerical simulations is a hard computational problem, currently bounded by the large size of the produced results. This book chapter is about using in situ techniques to enable large scale uncertainty quantification studies. We provide a comprehensive description of Melissa, a file avoiding, adaptive, fault-tolerant, and elastic framework that computes in transit statistical quantities of interest. Melissa currently implements the on-the-fly computation of the statistics necessary for the realization of large scale uncertainty quantification studies: moment-based statistics (mean, standard deviation, higher orders), quantiles, Sobol' indices, and threshold exceedance.

Published
2022
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38. An info-gap framework for robustness assessment of epistemic uncertainty models in hybrid structural reliability analysis

Author

Antoine Ajenjo, Emmanuel Ardillon, Vincent Chabridon, Bertrand Iooss, Scott Cogan, Emeline Sadoulet-Reboul, EDF R&D (EDF R&D), EDF (EDF), Institut FEMTO-ST, CNRS/UFC/ENSMM/UTBM, Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], epistemic uncertainty, hybrid structural reliability, Building and Construction, robustness, info-gap, Safety, Risk, Reliability and Quality, random sets, Civil and Structural Engineering
Abstract

The main objective of this work is to study the impact of the choice of input uncertainty models on robustness evaluations for probabilities of failure. Aleatory and epistemic uncertainties are jointly propagated by considering hybrid models and applying random set theory. The notion of horizon of uncertainty found in the info-gap method, which is usually used to assess the robustness of a model to uncertainty, allows to compare the bounds on the probability of failure obtained from different epistemic uncertainty models at increasing levels of uncertainty. Info-gap robustness and opportuneness curves are obtained and compared for the interval model, the triangular and trapezoidal possibility distributions, the probabilistic uniform distribution and the parallelepiped convex model on two academic examples and one industrial use-case. A specific demand value, as introduced in the info-gap method, is used as a value of information metric to quantify the gain of information on the probability of failure between less informative uncertainty models and a more informative ones.

Published
2021

39. Basics and Trends in Sensitivity Analysis: Theory and Practice in R

Author

Fabrice Gamboa, Bertrand Iooss, Sébastien Da Veiga, Clémentine Prieur, Safran Tech, Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), EDF (EDF), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Grenoble Alpes (UGA)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)

Subjects
Computer science, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Sensitivity (control systems), ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021
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41. A graph clustering approach to localization for adaptive covariance tuning in data assimilation based on state-observation mapping

Author

Didier Lucor, Bertrand Iooss, Angélique Ponçot, Sibo Cheng, Jean-Philippe Argaud, PERformance et prévention des Risques Industriels du parC par la simuLation et les EtudeS (EDF R&D PERICLES), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), DAtascience, trAnsition, Fluid instability, contrOl, Turbulence (DATAFLOT), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Mécanique-Energétique (M.-E.), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Université Paris-Saclay-Sorbonne Université - UFR d'Ingénierie (UFR 919), Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, [SPI.OTHER]Engineering Sciences [physics]/Other, Computer science, Covariance matrices, 0208 environmental biotechnology, Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, 010502 geochemistry & geophysics, 01 natural sciences, Measure (mathematics), Statistics - Computation, Unsupervised learning, Article, Mathematics (miscellaneous), Data assimilation, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, [STAT.CO]Statistics [stat]/Computation [stat.CO], Computation (stat.CO), 0105 earth and related environmental sciences, Clustering coefficient, Graph community detection, Covariance, Linear subspace, 020801 environmental engineering, Term (time), Scalability, General Earth and Planetary Sciences, Algorithm
Abstract

An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

Published
2021

42. Mesures d'importance relative par décomposition de la performance de modèles de régression

Author

Marouane Il Idrissi, Bertrand Iooss, Vincent Chabridon, Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Régression logistique, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Mesures d'importance, Shapley, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Régression linéaire
Abstract

International audience; En apprentissage statistique supervisé, les mesures d'importance relative ont pour but de quantifier de manière interprétable l'importance des covariables sur la sortie du modèle d'apprentissage, notamment en présence de dépendance entre ces covariables. Dans ce papier, deux mesures particulières (les valeurs de Shapley et les valeurs proportionnelles) sontétudiées. Ces mesures sont inspirées de deux solutions d'allocations issues de la théorie des jeux. Leurs liens avec d'autres mesures connues en régression linéaire (LMG et PMVD) sont présentés. Après une première illustration de leur formulation analytique dans le cas linéaire gaussienà deux variables, leur estimation pratique, dans un contexte de régression logistique, sur un jeu de données public de prévision des feux de fôret (Algerian Forest Fires) est proposée et discutée.

Published
2021

43. The Future of Sensitivity Analysis: An Essential Discipline for Systems Modelling and Policy Making

Author

Takuya Iwanaga, Saman Razavi, Hoshin V. Gupta, Clémentine Prieur, Joseph H. A. Guillaume, Elmar Plischke, Xifu Sun, John D. Jakeman, Anthony Jakeman, Holger R. Maier, Bertrand Iooss, Stefan Smith, Vincent Chabridon, Samuele Lo Piano, Nasim Hosseini, Masoud Asadzadeh, Qingyun Duan, R. Sheikholeslami, William E. Becker, Emanuele Borgonovo, Arnald Puy, Stefano Tarantola, Andrea Saltelli, Sergei Kucherenko, Giovanni Rabitti, Nicola Melillo, University of Saskatchewan [Saskatoon] (U of S), Fenner School of Environment and Society, Australian National University (ANU), Universitat Oberta de Catalunya [Barcelona] (UOC), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Grenoble Alpes (UGA)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Bocconi University [Milan, Italy], Clausthal University of Technology (TU Clausthal), University of Reading (UOR), European Commission - Joint Research Centre [Ispra] (JRC), Sandia National Laboratories [Albuquerque] (SNL), Sandia National Laboratories - Corporation, University of Arizona, Department of Electrical, Computer and Biomedical Engineering [Pavia], University of Pavia, Department of Actuarial Mathematics and Statistics [Edinburgh], Heriot-Watt University [Edinburgh] (HWU), Hohai University, University of Oxford [Oxford], University of Manitoba [Winnipeg], Department of Ecology and Evolutionary Biology [Princeton], Princeton University, University of Bergen (UiB), Imperial College London, University of Adelaide, Chercheur indépendant, Università degli Studi di Pavia = University of Pavia (UNIPV), University of Oxford, University of South Australia [Adelaide], School of Environment and Sustainability, Department of Decision Sciences, Bocconi University, The University of Arizona, Tucson, AZ, USA, Università degli Studi di Pavia, COLLEGE OF HYDROLOGY AND WATER RESOURCES HOHAI UNIVERSITY NANJING CHN, Partenaires IRSTEA, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Environmental Change Institute, Imperial College London, Department of Chemical Engineering, and School of Civil Environmental and Mining Engineering [Adelaide]

Subjects
Warrant, Environmental Engineering, 010504 meteorology & atmospheric sciences, Computer science, Management science, Ecological Modeling, 0208 environmental biotechnology, Context (language use), 02 engineering and technology, Systems modeling, 01 natural sciences, Structuring, 020801 environmental engineering, Variety (cybernetics), Multidisciplinary approach, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [SDE]Environmental Sciences, Uncertainty quantification, Software, 0105 earth and related environmental sciences
Abstract

International audience; Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.

Published
2021
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44. Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

Author

Vincent Chabridon, Bertrand Iooss, Marouane Il Idrissi, Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Mathematical optimization, Environmental Engineering, Coronavirus disease 2019 (COVID-19), Computer science, River flood, Monte Carlo method, Mathematics - Statistics Theory, 010103 numerical & computational mathematics, Statistics Theory (math.ST), 01 natural sciences, Statistics - Applications, Sobol' indices, Field (computer science), Methodology (stat.ME), 010104 statistics & probability, sensitivity analysis, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Applications (stat.AP), reliability analysis, Sensitivity (control systems), 0101 mathematics, Shapley effects, Reliability (statistics), Analysis method, Statistics - Methodology, [STAT.AP]Statistics [stat]/Applications [stat.AP], Critical event, Ecological Modeling, input correlation, [STAT.ME]Statistics [stat]/Methodology [stat.ME], Software
Abstract

International audience; Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relative to events which characterize the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called ``target Shapley effects'', allowing for interpretable sensitivity measures under dependent inputs. Two algorithms (one based on Monte Carlo sampling, and a given-data algorithm based on a nearest-neighbors procedure) are proposed for the estimation of these target Shapley effects based on the $\ell^2$ norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, the application of these new indices in two real-world use-cases (a river flood model and a COVID-19 epidemiological model) is discussed.

Published
2021

45. Robust tuning of Robbins-Monro algorithm for quantile estimation - Application to wind-farm asset management

Author

Bertrand Iooss, Jérôme Lonchampt, Iooss, Bertrand, Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), and Centre National de la Recherche Scientifique (CNRS)

Subjects
Estimation, Online statistics, business.industry, Computer science, Robbins-Monro, Uncertainty, Averaging, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Operations and Maintenance, Econometrics, Asset management, business, Offshore wind, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Quantile
Abstract

International audience; In uncertainty quantification of numerical simulation model outputs, the classical approaches for quantile estimation requires the availability of the full sample of the studied variable. This approach is sometimes not suitable as large ensembles of simulation runs need to gather a prohibitively large amount of data and computer memory. This problem can be solved thanks to an on-the-fly (iterative) approach based on the Robbins-Monro algorithm. We numerically study this algorithm for estimating a discretized quantile function from samples of limited size (a few hundreds observations). We also define "robust" values of the algorithm parameters in two practical situations: when the final number of the model runs N is a priori fixed and when N is unknown in advance (it can then be minimized during the study in order to save cpu time cost). This method is applied to the estimation of indicators in the field of engineering asset management for offshore wind generation. We show how the proposed algorithm improves the efficiency of the tool to support risk informed decision making in the field of offshore wind generation.

Published
2021

46. Prediction of crack propagation kinetics through multipoint stochastic simulations of microscopic fields

Author

Emilien Burger, Bertrand Iooss, Chu Mai, Etienne Le Mire, Matériaux et Mécanique des Composants (EDF R&D MMC), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
010302 applied physics, Propagation time, Crack propagation, Fracture mechanics, 02 engineering and technology, Mechanics, 021001 nanoscience & nanotechnology, lcsh:TK9001-9401, 01 natural sciences, random microstructures, Finite element method, Microscopic scale, Physics::Geophysics, Stress (mechanics), Dijkstra's algorithm, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0103 physical sciences, Shortest path problem, lcsh:Nuclear engineering. Atomic power, Stress corrosion cracking, multipoint stochastic simulation, 0210 nano-technology, Mathematics
Abstract

International audience; Prediction of crack propagation kinetics in the components of nuclear plant primary circuits undergoing Stress Corrosion Cracking (SCC) can be improved by a refinement of the SCC models. One of the steps in the estimation of the time to rupture is the crack propagation criterion. Current models make use of macroscopic measures (e.g. stress, strain) obtained for instance using the Finite Element Method. To go down to the microscopic scale and use local measures, a two-step approach is proposed. First, synthetic microstructures representing the material under specific loadings are simulated, and their quality is validated using statistical measures.Second, the shortest path to rupture in terms of propagation time is computed, and the distribution of those synthetic times to rupture is compared with the time to rupture estimated only from macroscopic values.The first step is realized with the cross-correlation-based simulation (CCSIM), a multipoint simulation algorithm that produces synthetic stochastic fields from a training field. The Earth Mover's Distance is the metric which allows to assess the quality of the realizations.The computation of shortest paths is realized using Dijkstra's algorithm. This approach allows to obtain a refinement in the prediction of the kinetics of crack propagation compared to the macroscopic approach. An influence of the loading conditions on the distribution of the computed synthetic times to rupture was observed, which could be reduced through a more robust use of the CCSIM.

Published
2021

47. BEPU robustness analysis via perturbed-law based sensitivity indices

Author

Vincent Larget, Vanessa Vergès, Bertrand Iooss, Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Direction Technique (EDF Direction Technique), EDF (EDF), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, Computer simulation, Computer science, 0211 other engineering and technologies, Perturbation (astronomy), 02 engineering and technology, Computer experiment, 020303 mechanical engineering & transports, 0203 mechanical engineering, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Law, Probability distribution, 021108 energy, Uncertainty quantification, Safety, Risk, Reliability and Quality, Loss-of-coolant accident, Importance sampling, Quantile
Abstract

One of the most critical hypothesis in BEPU studies is the choice of the probability distributions of uncertain input variables which are propagated through a numerical model. Depending on the method used for this choice, the probability density functions (pdf) for these variables are established with various levels of confidence, not always well known. Hence, bringing stringent justifications to the BEPU approach requires quantifying the impact of this second-level uncertainty (i.e. the uncertainty on the input variable pdf). To solve this problem, this paper deepens the robustness analysis based on the "Perturbed-Law based sensitivity Indices" (PLI). The PLI quantifies the impact of a perturbation of an input pdf on the quantity of interest (as a quantile of a model output or a safety margin) in the BEPU study. The mathematical formalism of the PLI is firstly applied to two particular quantities of interest: the quantile and the superquantile (which is the mean of the pdf tail exceeding the quantile). For both quantities, the PLI can be easily computed using a unique Monte-Carlo sample (ensemble of code runs) containing model inputs and output. Then, numerical tests are developed in order to define validity criteria of a PLI-based robustness analysis. The method is finally illustrated to the study of the thermal-hydraulic responses of a test facility during a cold leg Intermediate Break Loss Of Coolant Accident (IBLOCA) modelled using the calculation code CATHARE.

Published
2020
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48. SAPIUM: a generic framework for a practical and transparent quantification of thermal hydraulic code model input uncertainty

Author

Jinzhao Zhang, Guillaume Damblin, Francesc Reventos, Mathieu Couplet, Jean Baccou, Nils Sandberg, Bertrand Iooss, Philippe Fillion, Takeshi Takeda, Alessandro Petruzzi, T. Skorek, Deog-Yeon Oh, Rafael Mendizábal, Laboratoire de statistique et des modélisations avancées (IRSN/PSN-RES/SEMIA/LSMA), Service de Maîtrise des Incidents et Accidents (IRSN/PSN-RES/SEMIA), Institut de Radioprotection et de Sûreté Nucléaire (IRSN)-Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Tractebel engineering, CEA, NINE, CSN, Universitat Politècnica de Catalunya [Barcelona] (UPC), GRS, EDF R&D, KINS, NRA, Organisation de Coopération et de Développement Economiques = Organisation for Economic Co-operation and Development (OCDE), PSN-RES/SEMIA/LSMA, Institut de Radioprotection et de Sûreté Nucléaire (IRSN), and OECD/NEA

Subjects
biology, 010308 nuclear & particles physics, Computer science, 0211 other engineering and technologies, Control engineering, 02 engineering and technology, biology.organism_classification, 7. Clean energy, 01 natural sciences, law.invention, Thermal hydraulics, [SPI]Engineering Sciences [physics], Nuclear Energy and Engineering, law, 0103 physical sciences, Nuclear power plant, Code (cryptography), Key (cryptography), 021108 energy, Sapium, Uncertainty analysis
Abstract

International audience; Uncertainty analysis (UA) is a key element in nuclear power plant (NPP) deterministic safety analysis using best-estimate thermal hydraulic codes and best estimate plus uncertainty (BEPU) methodologies. If forward uncertainty propagation methods have now become mature for industrial applications, the input uncertainties quantification (IUQ) on the physical models still requires further investigations. The OECD/NEA PREMIUM project attempted to benchmark the available IUQ methods, but observed a strong user-effect due to lack of best practices guidance. The SAPIUM project has been proposed towards the construction of a clear and shared systematic approach for input uncertainty quantification. The main outcome of the project is a first “good practices” document that can be exploited for safety study in order to reach consensus among experts on recommended practices as well as to identify remaining open issues for further developments. This paper describes the systematic approach that consists in five elements in a step by step approach to perform a meaningful model input uncertainty quantification and validation as well as some “good practice guidelines” recommendations for each step.

Published
2020
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49. The ICSCREAM methodology: Identification of penalizing configurations in computer experiments using screening and metamodel -- Applications in thermal-hydraulics

Author

Vincent Chabridon, Bertrand Iooss, Amandine Marrel, CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), ANR-20-CE46-0013,SAMOURAI,Optimisation, analyse d'incertitudes et de fiabilité basées sur des simulations et des méta-modèles(2020), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Département Etude des Réacteurs (DER), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), and SIAM

Subjects
FOS: Computer and information sciences, Mathematical optimization, Computer science, 020209 energy, Mathematics - Statistics Theory, 02 engineering and technology, Statistics Theory (math.ST), 01 natural sciences, 7. Clean energy, Uncertainty quantification UQ, Computational Engineering, Finance, and Science (cs.CE), 010104 statistics & probability, symbols.namesake, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Global Sensitivity Analysis, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0202 electrical engineering, electronic engineering, information engineering, Metamodel, FOS: Mathematics, Use case, IB-LOCA, 0101 mathematics, Uncertainty quantification, Gaussian process, Computer Science - Computational Engineering, Finance, and Science, HSIC, [STAT.AP]Statistics [stat]/Applications [stat.AP], Probabilistic logic, Inversion, Conditional probability, Computer experiment, Metamodeling, Identification (information), Nuclear Energy and Engineering, Uncertainty propagation, symbols, Screening, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

In the framework of risk assessment in nuclear accident analysis, best-estimate computer codes, associated to a probabilistic modeling of the uncertain input variables, are used to estimate safety margins. A first step in such uncertainty quantification studies is often to identify the critical configurations (or penalizing, in the sense of a prescribed safety margin) of several input parameters (called “scenario inputs”), under the uncertainty on the other input parameters. However, the large CPU-time cost of most of the computer codes used in nuclear engineering, as the ones related to thermal-hydraulic accident scenario simulations, involve to develop highly efficient strategies. This work focuses on machine learning algorithms by the way of the metamodel-based approach (i.e., a mathematical model which is fitted on a small-size sample of simulations). To achieve it with a very large number of inputs, a specific and original methodology, called ICSCREAM (Identification of penalizing Configurations using SCREening And Metamodel), is proposed. The screening of influential inputs is based on an advanced global sensitivity analysis tool (HSIC importance measures). A Gaussian process metamodel is then sequentially built and used to estimate, within a Bayesian framework, the conditional probabilities of exceeding a high-level threshold, according to the scenario inputs. The efficiency of this methodology is illustrated on two high-dimensional (around a hundred inputs) thermal-hydraulic industrial cases simulating an accident of primary coolant loss in a pressurized water reactor. For both use cases, the study focuses on the peak cladding temperature (PCT) and critical configurations are defined by exceeding the 90%-quantile of PCT. In both cases, the ICSCREAM methodology allows to estimate, by using only around one thousand of code simulations, the impact of the scenario inputs and their critical areas of values.

Published
2020
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50. Parseval inequalities and lower bounds for variance-based sensitivity indices

Author

Fabrice Gamboa, Bertrand Iooss, and Olivier Roustant

Subjects
derivative-based global sensitivity measures, Statistics and Probability, Polynomial chaos, Chaos expansion, Poincaré inequality, Sobol sequence, Sobol-Hoeffding decomposition, Function (mathematics), Differential operator, Parseval's theorem, symbols.namesake, 65C60, Hilbert basis, 62P30, symbols, Applied mathematics, Truncation (statistics), Statistics, Probability and Uncertainty, Sobol indices, 26D10, Mathematics
Abstract

The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol’ sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol’ indices with Parseval equalities and give general lower bounds for these indices obtained by truncation. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.

Published
2020
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